This invention relates to interferometric auto-correlation and, more particularly, to interferometric auto-correlation using third-order nonlinearities.
Interferometric auto-correlation (IAC) measurements are used frequently to determine the pulse-width as well as the frequency chirp on ultrashort pulses (e.g. between 1 ps to 10 fs) from continuous-wave (cw) modelocked lasers. This type of measurement conventionally uses second-harmonic generation (SHG) in a Michelson interferometer. In the Michelson interferometer, an incoming train of pulses is split into two beams that are directed along two arms of the interferometer. Upon retro-reflection from mirrors or corner-cubes that introduce a variable delay in one of the beams, the two beams are recombined co-linearly at the beam splitter. Thus, the optical field exiting the interferometer (combined beams) is written as: EQU E=E.sub.1 +E.sub.2 =E.sub.0 (t) cos (.omega.t+.phi.(t))+.alpha.E.sub.0 (t+.tau.) cos (.omega.t+.omega..tau.+.phi.(t+.tau.)), Eqn. (1)
where E.sub.0 is the amplitude function of the pulse, .omega. is the frequency, .phi. is the phase (including the chirp) of the pulse, .tau. is the delay, and .alpha. is the ratio of the two field amplitudes.
The field represented by Eqn. (1), when focused into a second-harmonic (SHG) crystal, produces light at a frequency 2.omega., whose irradiance (in the low conversion limit) is proportional to the square of the incident irradiance: EQU I.sub.2.omega. .varies.I.sub..omega..sup.2 =.vertline.E.vertline..sup.4
Since the detector measures a time average (over .congruent.100 ns time scale) the measured quantity is: S.sub.nl (.tau.)=.intg.I.sub.2.omega. dt. Normalizing this quantity and using the normalized irradiance envelope function .function.(t).varies.E.sub.0.sup.2 (t), S.sub.nl (.tau.) becomes ##EQU1## which is normalized to a.sup.2 .intg..function..sup.2 (t)dt=1, and where .DELTA..phi.(t,.tau.)=.phi.(t+.tau.)-.phi.(t). In Eqn. (2) the first integral represents the intensity auto-correlation, while the remaining integrals are interferometric terms containing information about the phase, i.e., the chirp, of the laser pulse.
Real-time measurement of S.sub.nl (.tau.) is obtained by mounting the retro-reflector of the delay arm on a speaker, which is driven by a low frequency (20-50 Hz) sinusoidal voltage. Then, the displacement of the reflector due to vibration of the speaker is x=x.sub.0 sin (.OMEGA.t), leading to a variable round-trip delay of .tau.=2(x.sub.0 /c) sin (.OMEGA.t).congruent.2x.sub.0 .OMEGA.t/c. The .omega..tau. terms in Eqn. (2) can be written in real time as .omega.'t, where .omega.'.congruent.2x.sub.0 .OMEGA..omega./c=2(.nu./c).omega. and v is the velocity of the speaker vibration at its zero crossing. This configuration allows IAC traces of cw modelocked laser pulse trains to be viewed directly on an oscilloscope. By adjusting .OMEGA. and x.sub.0 (i.e., the voltage swing on a speaker driver) .omega.' is controlled. Typical values are between 0.5 to 2 MHz. Note that, to observe fringes, the detection system has to be fast compared to the period of the oscillations (2 to 0.5 .mu.s.
The SHG method has a large signal-to-noise ratio since there is no linear background present. But it requires a phase-matchable second order nonlinear crystal. Furthermore, in the femtosecond regime, group velocity mismatch between .omega. and 2.omega. (beams imposes a limit on the thickness of the nonlinear crystal. For example, using LilO.sub.3 in order to measure 50 fs pulses, a crystal having a thickness &lt;100 .mu.s should be used. This restriction in thickness, in turn, limits the amount of generated 2.omega. power, and, hence, sensitive detectors such as photo-multiplier tubes (PMT) are required. Together, the SHG crystal and the detection system are costly devices.
In accordance with the present invention, third-order nonlinearities are used to provide an auto-correlator that is wavelength agile (always phase matched) without the use of SHG crystals.
Additional objects, advantages and novel features of the invention will be set forth in part in the description which follows, and in part will become apparent to those skilled in the art upon examination of the following or may be learned by to practice of the invention. The objects and advantages of the invention may be realized and attained by means of the instrumentalities and combinations particularly pointed out herein.